How Do Household Preferences Shape Economic Models?

Table of Links

Abstract

1 Introduction

2 Mathematical Arguments

3 Outline and Preview

4 Calvo Framework and 4.1 Household’s Problem

4.2 Preferences

4.3 Household Equilibrium Conditions

4.4 Price-Setting Problem

4.5 Nominal Equilibrium Conditions

4.6 Real Equilibrium Conditions and 4.7 Shocks

4.8 Recursive Equilibrium

5 Existing Solutions

5.1 Singular Phillips Curve

5.2 Persistence and Policy Puzzles

5.3 Two Comparison Models

5.4 Lucas Critique

6 Stochastic Equilibrium and 6.1 Ergodic Theory and Random Dynamical Systems

6.2 Equilibrium Construction

6.3 Literature Comparison

6.4 Equilibrium Analysis

7 General Linearized Phillips Curve

7.1 Slope Coefficients

7.2 Error Coefficients

8 Existence Results and 8.1 Main Results

8.2 Key Proofs

8.3 Discussion

9 Bifurcation Analysis

9.1 Analytic Aspects

9.2 Algebraic Aspects (I) Singularities and Covers

9.3 Algebraic Aspects (II) Homology

9.4 Algebraic Aspects (III) Schemes

9.5 Wider Economic Interpretations

10 Econometric and Theoretical Implications and 10.1 Identification and Trade-offs

10.2 Econometric Duality

10.3 Coefficient Properties

10.4 Microeconomic Interpretation

11 Policy Rule

12 Conclusions and References

Appendices

A Proof of Theorem 2 and A.1 Proof of Part (i)

A.2 Behaviour of ∆

A.3 Proof Part (iii)

B Proofs from Section 4 and B.1 Individual Product Demand (4.2)

B.2 Flexible Price Equilibrium and ZINSS (4.4)

B.3 Price Dispersion (4.5)

B.4 Cost Minimization (4.6) and (10.4)

B.5 Consolidation (4.8)

C Proofs from Section 5, and C.1 Puzzles, Policy and Persistence

C.2 Extending No Persistence

D Stochastic Equilibrium and D.1 Non-Stochastic Equilibrium

D.2 Profits and Long-Run Growth

E Slopes and Eigenvalues and E.1 Slope Coefficients

E.2 Linearized DSGE Solution

E.3 Eigenvalue Conditions

E.4 Rouche’s Theorem Conditions

F Abstract Algebra and F.1 Homology Groups

F.2 Basic Categories

F.3 De Rham Cohomology

F.4 Marginal Costs and Inflation

G Further Keynesian Models and G.1 Taylor Pricing

G.2 Calvo Wage Phillips Curve

G.3 Unconventional Policy Settings

H Empirical Robustness and H.1 Parameter Selection

H.2 Phillips Curve

I Additional Evidence and I.1 Other Structural Parameters

I.2 Lucas Critique

I.3 Trend Inflation Volatility

4.2 Preferences

The focus is on well-behaved models that readily generate unique interior solutions, to this end, I make several intuitive restrictions on preferences. To do so, I make several intuitive restrictions. To this end, u ′ > 0 so agents always wish to consume more and the transversality condition will bind with equality. u ′′ < 0 to incentivize consumption smoothing. It is costly for agents to work ν ′ > 0, ν ′′ > 0 encourages the agent to balance work and leisure.[22] Together these conditions ensure uniqueness of interior solutions to the agent’s optimization at any point in time with a non-stochastic background.

Additional conditions are required to rule out boundary solutions. The standard Inada condition for consumption is

along with zero net wealth. This ensures the representative household will always work. To force them to take leisure

σ represents the coefficient of relative risk aversion. It is also the inverse of the elasticity of inter-temporal substitution. η is the inverse Frisch elasticity of labor supply. For the empirical part I will work with the popular functional forms. This ensures these parameters are structural and do not vary with income allowing comparison with standard econometric estimates.[23]

Each firm produces an individual variety for which demand is given by

θ is the elasticity of demand. Appendix B.1.1 details the underlying optimization problem.

[22] Alternatively, we could imagine leisure is a good in demand that represents an opportunity cost of working. It will be convenient to do so in one proof discussed in the Appendix (C.1.2)